Problem: Which of the following numbers is a factor of 180? ${8,9,11,13,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $180$ by each of our answer choices. $180 \div 8 = 22\text{ R }4$ $180 \div 9 = 20$ $180 \div 11 = 16\text{ R }4$ $180 \div 13 = 13\text{ R }11$ $180 \div 14 = 12\text{ R }12$ The only answer choice that divides into $180$ with no remainder is $9$ $ 20$ $9$ $180$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $180$ $180 = 2\times2\times3\times3\times5 9 = 3\times3$ Therefore the only factor of $180$ out of our choices is $9$. We can say that $180$ is divisible by $9$.